Inhomogeneous ordering in weakly coupled Heisenberg $S=1/2$ chains with random bonds

Long range magnetic ordering in the quasi-one-dimensional random-bond antiferromagnet BaCu$_2$(Si$_{1-x}$Ge$_{x}$)$_2$O$_7$ is studied in $mu$SR experiments as a function of disorder strength. Compared to the disorder-free parent materials, the saturation ordered moment is found to be considerably reduced. Moreover, even in weakly disordered species, the magnetically ordered state is shown to be highly inhomogeneous. The results are interpreted in terms of weakly coupled random spin chains, governed by the ``infinite randomness`` fixed point.